0 Introduction

The open cracks are often rich in fluids and provide a pass way for hydrocarbon migration, so accurate identification of cracks has become a very critical technical aspect in hydrocarbon exploration and development. Detailed information on the distribution of cracks and strength helps to determine the optimum drilling location. For azimuthal anisotropic media, velocity, travel time difference and amplitude change with azimuth. The seismic response from different directions is different, which is influenced by lithology, pore fluid, and anisotropy of media.

同时，国务院有关部门在食品工业产品价格、税收、资金使用、固定资产折旧与进出口等方面开始制定一系列优惠政策，以更全面、明确的政策指导与规则制定推动着食品工业的增速由低速转向中高速。

Because of the presence of cracks, the fractured reservoirs exhibit anisotropic characteristics. The longitudinal wave propagates in the cracked media not only has the directional characteristics, but also has many propagation properties such as velocity, reflection coefficient, frequency, etc., which vary with the observation angle, and these variations are related to the direction of the crack and the strength of the crack. Therefore, the seismic characteristic parameters of the wide azimuthal P-wave seismic wavelengths collected on the ground are regularly changed with the observation azimuth and offset distance in the fractured reservoir. It is possible to achieve qualitative and even quantitative estimation of the trend of the cracks, the density of cracks and the fluid in the cracks, and achieve the crack prediction by detecting the variation of these characteristic parameters in the P-wave data. In recent years, geophysicists have proposed a variety of crack detection methods based on P-wave reflection data. These methods can be divided into two categories: the first category is the amplitude variation with the offset and azimuth (AVAZ), (Lynn et al., 1996; Ruger, 1998; Gray et al., 2000), the second category is velocity variation with azimuth (VVAZ), (Tsvankin, 1997; Li, 1997; Grechka & Tsvankin, 1998; Zheng, 2006). Both can be described as attribute variation with direction (AVD) technology.

The anisotropy of the rock refers to the variation of physical properties of the rock with the direction. In the formation, there are many sources of anisotropy, such as the inherent anisotropy of the rock, the presence of pores and cracks in different shapes and sizes in the rock, different types of fluid filling in the cracks, etc. In particular, the anisotropy in the seismology is mainly manifested in the velocity of seismic waves in different directions.

这天，小熊欢欢在他的房间里擦拭他最喜欢的玩具机器人。明天是弟弟乐乐的生日，欢欢想把这个机器人作为生日礼物送给弟弟。

Then the effective elastic constant of the filler medium can be applied to the method proposed by Eshelby (1957) to find the frequency of the mediumrelaying on the effective elastic tensor and simulate the frequency-dependent velocity and quality factor Q：

The authors study and develop the travel forward modeling method in anisotropic media and combine it with the latest petrophysical model. The variation of P-wave reflection time with azimuth angle, offset and crack angle is simulated for gas-bearing and water-bearing fissures, with some useful conclusions achieved.

Among them, the anisotropy strength of qP wave is represented by ε, and the larger ε value indicates stronger P-wave anisotropy. The velocity of the qP wave in the near vertical direction is represented by δ, and the anisotropic intensity of the qS wave is represented by γ, and its value represents the intensity of the shear wave anisotropy. The Thomsen parameter not only describes the physical meaning of anisotropy, but also establishes a theoretical evidence for the inversion of anisotropic parameters through seismic attributes.

1 HTI media introduction

The complexity of sedimentary environment and geological process determines the diversity of cracks in the rocks. There are several types of cracks in terms of shape: vertical parallel, horizontal, orthogonal, skewed, inclined, random, etc. In the past decade, the most widely studied models are the media with periodically deposited thin layers and the media with vertically oriented cracks, which are transversely isotropic media. TI medium, defined as transverse isotropy medium, is the elastic medium with isotropic surfaces. Its elastic properties are equivalent to that of the hexagonal crystal system, with five independent elastic parameters, four of which are physically related to the azimuthal velocity of longitudinal and transverse waves. When the symmetry axis of TI medium coincides with Z-axis, it is called a VTI medium, which can approximately simulate the transverse isotropy exhibited by the periodically deposited thin interlaminar layers in horizontally layered media, and when the symmetry axis of the media of TI coincides with the X or Y axis, it is called the HTI media. The HTI media model can simulate the anisotropy caused by the vertical crack group in the stress-producing space, which is also called the anisotropic media or EDA (Extensive Dilatancy Anisotropy) media (Fig. 1), and HTI media is the most typical one in azimuthal anisotropy media. In addition, when the media is a combination of VTI and HTI, its elastic properties are equivalent to those of an orthorhombic system with nine independent elastic parameters. In summary, seismic waves propagate in these typical media with their own unique laws because of their different elastic parameters.

Its elastic tensor is：

(1)

Hudson gives a basic assumption that the fluid is confined within the fissure and that the fluid does not communicate with each other. This assumption has no effect on the fissure, but in other cases it is always affected. Thomsen (1998) developed this model, assuming that the medium contains a set of parallel fissures that are hydraulically connected to an equal pore diameter and that the fluid pressure is locally balanced. Thomsen gives another set of parameters to describe the nature of the crack, including the parameters α, β, ε, δ, γ and which are defined as:

(2)

The following are the P-wave and S-wave velocities in the direction of symmetry axis and the Thomsen anisotropy parameters:

虽然大事记的收录标准和编写规定在志书编纂规则中有明确规定，但编者面对志书中的各种实际问题，具体的收录与删增是以编者对事情的认识和编纂水平决定的，所以，编者一方面要熟悉各种标准规范，一方面要通读全志，内心要有正确的衡量标准，小心斟酌、细心思考，对资料要注意保存备查，对内容要进行前后反复核对修定，以使全志的时间及相关资料前后统一。

(3)

浮置型梯子式轨道结构，由混凝土纵梁和左右纵梁之间的钢制横向弹性连接件组成“梯子式”的一体化结构，并在纵向轻轨之间进行减振支撑，该轨道结构由于重量小，维护方便等特点主要用于在城市轨道的高架桥。

2 Travel time characteristics of azimuthal anisotropy in HTI media

The pore space of the model consists of three parts: spherical pore (porosity is φp), centimeter-level micro-fissure (density is εc) and m-level crack (density is εf, radius is αf). Fissure density is calculated as where N is the number of fissures contained in volume V,α is the fissure radius. The radius of micro-fractures and pores is equal to the particle size ζ. The model uses the time scale factor to characterize the pore pressure time scale of the parameter τ. Its physical meaning is the time required for the crack system squeezed by the seismic wave to restore the balance. The time scales for fissuresand cracks are denoted by τm and τf, respectively:

Where Kf1 is the volume modulus of the fluid, Vf1 is the shear wave velocity, the density of the saturated rock and the pore fluid is ρ and ρf1.

(4)

Δt(φ,x)can be written as：

Δt(φ,x)=(t⊥-t||)cos2φ=B0(x,ε,δ)cos2φ

(5)

(6)

Since B0(x,ε,δ) is independent of the azimuth angle, it can be seen from the equation that AMR can be regarded as a function of cos2φ for fixed gun spacing under weak anisotropy conditions. This characteristic of AMR allows us to infer the direction of crack directly without having to know t⊥ and t||.

3 Calculation method of dual-phase medium velocity

In this way, according to the frequency-dependent elastic tensor calculated by the Chapman model, the elastic tensor of any TTI medium can be obtained by Bond conversion.Then the phase velocity of the seismic waves propagating in any direction can be calculated by the Christoffel equation and the frequency-dependent velocity and quality factor can be calculated. As shown in Fig. 3 and Fig. 4.

In many cases, the exploration seismology needs to solve the problem of longitudinal wave crack detection in multi-layered HTI media, especially when the reservoir is covered by multi-layered media with cracks. In response to this problem, using the response of the azimuth time difference of the longitudinal waves on orthogonal seismic lines (AMR: Azimuthal Moveout Response), a stripping method of the multi-layered HTI medium is introduced. Taking into account the case of fixed offset, the target layer of crack development AMR is a function of cos2(α-φi), where α is the azimuth between the layers and φi is the azimuth of the crack. By calculating and extracting the AMR on the one-dimensional orthogonal line, we can get the layer crack direction φi by intersection analysis. The delamination method can be obtained by the remaining amount of dynamic correction of the layer top interface of the target layer. In this paper, we first introduce the concept of AMR and derive their calculation formulas. Based on this, the longitudinal wave crack detection in multi-layer HTI media is realized by the planar method.

北方气候干燥，南方气温偏高，均不适合农作物生长。据统计，植物通常适合生长在一定温度和湿度的环境下[3]。然而，很多情况下，植物因无法在这种种植环境下生长，导致成活率降低[1-3]。因此，在农作物生长过程中，保持农作物的温度和湿度是一个十分重要的问题。

(7)

(8)

Where ζ is the particle size, κ is the permeability, η is the fluid viscosity coefficient,define parameter σc:

（4）囊性卵巢癌总计6例，肿瘤壁厚度不一，肿瘤内实质性的成分和乳头状结占比较多，T1WI及T2WI均呈现低信号、等信号及等信号、高信号混合的信号。

(9)

Where μ is the shear modulus, r is the aspect ratio of the crack, and υ is the aspect ratio of the fissure.Introduce the following parameters:

(10)

(11)

(12)

(13)

First of all, supposing the angles between the two mutually orthogonal lines passing through the same CMP point and the strike of the crack are φi and π/2-φ respectively, as shown in Fig. 2. The azimuthal response (AMR) of the single-layer HTI media at the CMP point can then be defined as the travel time difference of the single reflected seismic wave on the bottom of the single-layered HTI media on these two orthogonal lines.

In the small aspect ratio hypothesis(r<10-2), Chapman et al. (2003) give a time scale factor approximation:

(14)

In the fractured reservoirs, because of the compaction from overlying layers, only high-angle or near-vertical cracks can be preserved, and the anisotropic characteristics of the seismic wave are mostly caused by these cracks. For the medium with vertical cracks, it can be taken as a horizontal transverse isotropic (HTI) media. The use of the anisotropic characteristics of seismic waves helps to determine the reservoir characteristics of interest for vertical cracks.

(15)

(16)

Subsequently, Chapman (2003, 2006) proposed a fluid replacement method. The bulk modulus of the saturated fluid is the time scale τ0, the fissure density ε through a frequency ω0 and the seismic wave longitudinal wave and shear wave propagation speed can be expressed as:

The elastic tensor expression of the fluid saturated medium given by Chapman et al. (2006). Satisfies the following form:

(19)

Where the first term represents the isotropic rock skeleton elastic tensor without filler, and the latter three represent the contribution of fissures, pores and cracks, respectively. From the longitudinal and shear wave velocity of the rock Quasi-Lame coefficient can be obtained.

(20)

(21)

For rocks with only pores and fissures, if εf is set to zero, then the elastic tensor is:

(22)

Chapman introduces two parameters Λ and γ to satisfy

(23)

Thus, for any frequency, fluid bulk modulus, and time scale factor, the elastic tensor is:

(24)

Chapman et al. (2003) extended the jet model to have the characteristics of porous elasticity and proposed a microstructural porous elastic model. The solid phase of the model is a linear elastomer, which consists of ellipsoidal cracks and coin-shape pores, and the pore spaces are connected. Based on the jet mechanism, the model assumes that the squeezing action caused by the propagation of seismic waves causes free fluid exchange between the pores and the cracks. In 2003, Chapman continued to extend the model to two scales, namely, fissure scale and crack scale.

第四，决心维度。这一维度主要是指中国实现承诺的意志。2012年黄岩岛事件由菲律宾挑起而最终以中方实控这一岛屿及附近海域而告终。自2014年以来，尽管以美国为首的部分国家在各类场合不断要求中国停止对实控的7个岛屿进行的大规模吹填和建设项目，并且美国还以航行自由和地区稳定受到影响为由在上述岛屿附近进行了海上和空中巡航，并藉此加深与越菲等国的双边关系，但中国不为所动，坚定不移地完成了南海岛礁建设项目。对此，其他国家包括美国在内均无能为力。基于上述事件，国际社会已经充分意识到中国维护南海主权和海洋权益这一自身核心利益的决心。

Experiments show that with the increase of the fissure density and the high modulus and the degree of seismic wave dispersion gets greater. And the type of fluid directly determines the frequency range of the dispersion phenomenon. It can be observed from Fig. 3 that the range of the transition band depends on the fluidity of the crack fluid, and fluids with low fluidity require a longer time (larger time-scale factor) to reach new pressure equilibrium, so the dispersion mainly occurs in the low frequency band. The fluids with strong fluidity can reach a new pressure balance state in a very short period of time (smaller time scale factor), so the dispersion occurs mainly in the high frequency band. Fig. 4 shows the results of the model calculations of the three types of crack density.

The results show that the intensity of dispersion and attenuation increase with the increase of crack density that means the number of cracks per unit volume represent the development degree of cracks. The higher the degree of crack development, the greater the amount of fluid exchange in the process of seismic wave propagation, which leads to the stronger energy dissipation.

4 Numerical simulation

According to the above theoretical model, this paper simulate the azimuth time difference response in biphasic crack media, and analyze the influence of different crack parameters on the azimuth time difference response, including the filling fluid type and crack density, The experimental parameters are as follows: for time scale factor: water is 2×10-5 s, oil is 4×10-4 s, gas is 4×10-7 s; Water-bearing rock density is 2 150 kg/m3, oil-bearing rock density is 2 180 kg/m3, gas-bearing rock density is 2 076 kg/m3; Porosity is 0.1; crack density is 0.1, 0.2, 0.3 respectively. When the cracks in the case of containing oil, water, gas, and the simulation results are illustrated in Figs. 5,6,7:

Compared Fig. 5, Fig. 6 and Fig. 7, it can be found that: ① The relationship between AMR and azimuth angle shows a clear cosine curve; ② the increase of crack density increases the crack azimuth time difference as a whole, whereas the degree of AMR response transformation for each frequency component is substantially the same; ③ when the cracks are filled with fluid, the degree of AMR response from high to low is gas-bearing, water-bearing and oil-bearing. And the order of the degree of AMR difference from high to low under single frequency is oil-bearing, water-bearing and gas-bearing.

高河飞奔回屋子里，气喘如牛。原来，二表哥还不肯忘记那件事，他打算怎么样，威胁我？高河想到这里，不禁心惊肉跳。

(2)运用多种多媒体手段。如课程目标“铁碳合金相图及典型铁碳合金的平衡结晶过程”中,加热过程奥氏体化过程与冷却过程珠光体的形成等,在语言描述的同时,运用视频演示,给学生更直观的印象。运用微课和网络教学等,更好地促进学生对理论的理解,能获得较好的教学效果。

5 Conclusions

(1) The time difference of crack azimuth is strongly sensitive to both frequency and azimuth. The comprehensive analysis and study of its variation characteristics can provide a valuable reference for the study of underground fractured media.

(2) When there is fluid filling in the crack, in addition to the crack structure, the crack azimuth time difference property of seismic data is also greatly affected by fluid type.

(3) Considering the obvious frequency-dependent features exhibited by the azimuthally jetting properties when cracks contain fluids, it is believed that if frequency-division obtainment of the attribute can be selected, it will provide useful information for crack fluid identification.

References

Canning A, Malkin A. 2009. Automatic anisotropic velocity analysis for full azimuth gathers using AVAZ//SEG Technical Program Expanded Abstracts,201.

Chapman M. 2003. Frequency-dependent anisotropy due to meso-scale fractures in the presence of equant porosity. Geophysical Prospecting, 51(5): 369-379.

Chapman M, Liu E, Li X Y. 2006. The influence of fluid sensitive dispersion and attenuation on AVO analysis. Geophysical Journal International, 167(1): 89-105.

Liu C H, Wang X Z. 2011. The applications of wide azimuth seismic technique//International Geophysical Conference, Shenzhen, China, doi:10.1190/1.4704986.

Liu C, Li B N, Zhao X, et al. 2014. Fluid identification based on frequency-dependent AVO attribute inversion in multi-scale fracture media. Applied Geophysics, 11(4): 384-394.

Liang Z Q, Wang S X, Guo Q. 2013. P wave residual time difference crack detection technology based on TTI medium. Geophysical Prospecting for Petroleum, 52(4):347-353. (in Chinese with English abstract)

Liu J Y. 2010. Azimuthal anisotropy analysis and crack detection: master’s degree thesis. Chengdu: Chengdu University of Technology. (in Chinese with English abstract)

Ning Y L. 2012. Research on AVO method based on inverse spectral decomposition of dispersive medium: master’s degree thesis. Changchun: Jilin Univercity. (in Chinese with English abstract)

Qu S L, Ji Y X, Wang X, et al. 2001. Method for detecting P wave attribute crack in all directions. Petroleum Geophysical Exploration, (4): 390-397. (in Chinese with English abstract)

Sa L M. 2010. Seismic identification theory and method of fracture cavity type reservoir. Beijing : Petroleum Industry Press, 694. (in Chinese with English abstract)

Wang S, Li X Y. 2006. Layer stripping of azimuthal anisotropy from P-wave reflection moveout in orthogonal survey lines. Journal of Geophysics & Engineering, 3(1): 1-11.

Xiong J L, Liu Y, Hou B G. 2005. Arbitrary anisotropic medium azimuth travel time forward modeling. Oil Geophysical Prospecting, 40(3): 300-304. (in Chinese with English abstract)